People have a certain idea of how government should work, but from the outside we often don't see the real frictions that drive problems on the inside.
What are the best books that show how political dynamics really work?
To take just one example: how decisions in bureaucracies are limited by miscommunication, disorganization, poor record-keeping and other varieties of incompetence that are not typically thought of affect policy... how these issues affect the ability of political leaders to change things for the better.
Or how, in foreign relations, seemingly compassionate moves by one force may provoke counter-moves by other powers in the region... counterintuitively making the problem worse.
That sort of thing...
The thing is, I don't think this is really a history question; it's more of a political theory or political science question.
The interaction and interplay of rules and constraints, written and unwritten, legal and customary, that impact the behavior of individuals in government is one of the primary topics of study in the field of political science. And the way these things interact at the highest levels of state, particularly how they condition the interactions between states, is a major concern of the separate field of international relations. History informs a lot of the inferences that political scientists and international relations theorists make, however while historians are typically very concerned with evaluating and reinterpreting details, political scientists and international relations theorists typically try to extrapolate broad universal conclusions. This means that it is very difficult, or even impossible, to answer your questions from a historical perspective.
Political scientists and international relations theorists also differ from historians in methodology and approach, even though in the past two decades or so younger scholars have begun looking at smaller and more self-contained topics (sometimes to the displeasure of their older colleagues, who prefer to debate broad universal truths). In any case, a political scientist might begin a study asking a question like "What are the main questions and concerns behind the implementation of a healthcare policy?" and from this question will usually try to extrapolate a theoretical framework that policymakers and government workers can use to inform their decisions. A historian would be more interested in asking something like, "What factors drove a wedge between theory and practice in Italian healthcare policy between 1945 and the reform of 1978?" In this example, a journalist, politician, bureaucrat, or another academic handling an inquiry in the state of healthcare might do well to read both studies, and both examples certainly have a lot of overlap (if they were working at the same institution, these two hypothetical scholars would probably collaborate or at least inform and influence each other's work). However while the political scientist is interested in asking, "How does government really work?" the historian is asking, "How did government really work?"
But before you repost this to r/AskSocialScience, know that your question is also difficult to answer from a political science or international relations perspective. As you might imagine, focusing on conclusions (or, if necessary, lack thereof) means that there are multiple competing theories and schools of thought in the fields of political science and international relations. While historians also have their differences in ideas and approaches, historians seldom extrapolate views that they hold to be broad universal truths (although I suppose you can always make broad conclusions on human nature, but I digress). Historians are much more likely to qualify that their assertions are only valid insofar as they relate to context of the evidence they have examined. So what is indisputable in the history of the Mediterranean is not necessarily applicable when examining China or India: while scholars ask questions of the causes and qualities of the fall of the Roman Empire and rise of the Frankish Kingdom, these causes and qualities cannot be applied to the Sixteen Kingdoms period of Chinese history. To their credit, political scientists and international relations theorists are typically very careful about precise wording, and often qualify their conclusions with many caveats so that they are aligned with the evidence they present (things like "this is only valid for democracies," or even, "this is only valid for parliamentary democracies").
So you ask for reading material; I can suggest a few books that might interest you. The first part of your question, I think, is most addressed by the discipline of Public Administration Theory within Political Science. I have only really tangentially examined this in the historical setting, and wouldn't really know where to start introduction-wise. Although I'm biased towards my area of study, a book that I really like and recommend is Putnam et al's Making Democracy Work: Civic Traditions in Modern Italy (1992) which draws some general conclusions about civic government based on historical and empirical evidence collected in Italy. I'm actually better versed in the shorter second part of your question, and can recommend a few books on international relations strongly informed by historical analysis. They are: Mansbach's The Global Puzzle: Issues & Actors in World Politics (1994); Jackson's Global Politics in the Twenty-first Century, (2013); and if you can get a hold of it Dehio's The Precarious Balance: Four Centuries of the European Power Struggle (1965). Of the three I like Dehio's best, not just because because he's a pure historian. Although his book is old, his views are a surprising reflection of number of theories in the "Realist" school of International Relations, which influenced many of the the views inside American academia and government for some five decades after the Second World War.